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Q: Graph sketching questions/verify work ( Answered ,   0 Comments ) Question
 Subject: Graph sketching questions/verify work Category: Science > Math Asked by: jeremit-ga List Price: \$80.00 Posted: 09 Aug 2006 10:09 PDT Expires: 08 Sep 2006 10:09 PDT Question ID: 754306
 ```I just have a couple problems that I attempted and need to see if I did them correctly as well as how to come up with graphs for a couple. 1. I don't know how to sketch a graph of the height of the cork above the sea floor as a function of time. Im sure it's much simpler than im making it out to be. http://img308.imageshack.us/my.php?image=calcshit001ach9.jpg 2. Once again, How would I sketch a graph for the quantity of water in the reservoir as a function of time? How would I draw plausible graphs for the flow into and flow out of the reservoir for the first half of 1994 seeing as how the quantity of water in the reservoir was about the same as in January 1993? http://img308.imageshack.us/my.php?image=calcshit001boj9.jpg 3. Just need the work looked at on these two (I think I got them right): http://img347.imageshack.us/my.php?image=calcshitcox9.jpg http://img347.imageshack.us/my.php?image=calcshitbko4.jpg``` Clarification of Question by jeremit-ga on 09 Aug 2006 10:15 PDT ```I know the graphs don't have exact values, I just need to know what they would look like and to sketch them for future reference``` Request for Question Clarification by elmarto-ga on 09 Aug 2006 11:34 PDT ```Hello again jeremit, Could you please clarify what you need for question 2? Are you supposed to draw a graph only for the first half of 1994, given the 1993 graph you provided? At what point is the quantity of water supposed to be the same as in Jan 1993? Thank you very much, elmarto``` Clarification of Question by jeremit-ga on 09 Aug 2006 12:00 PDT ```I did draw the graph roughly, but the water level in the reservoir is supposed to be almost the same in Jan of 1993 as in Jan of 1994. And yes, I would need a couple plausible graphs for the flow of water into the reservoir and out of the reservoir for the first half of 1994 given the 1993 data provided.``` Subject: Re: Graph sketching questions/verify work Answered By: elmarto-ga on 09 Aug 2006 18:37 PDT Rated: ```Hello again jeremit, Most of your work is absolutely correct. I've spotted a small mistake in your graph for question 2, though. Question 1 I don't think this can be put any simpler than you did. The height of the cork above the sea floor as a function of time can certainly be described by a sinusoidal function, just as you did. Let's say, for example, that if the sea were calm, the cork would be 100 ft above the sea floor. A plausible function for the height of the cork could then be: Height(t) = sin(t) + 100 The question in the image you supplied asks about the vertical velocity of the cork rather than its height. Now, this velocity is simply the derivative of the height with respect to time. Following the example above, this yields: d(Height)/dt = cos(t) Since cosine is still a sinusoidal function, it's correct to graph the velocity as you did in your graph. Notice that it's important that this function crosses the x-axis (i.e. takes on negative values, as the cork moves both up and down), while the height function does not (as it's not possible for the cork to go below the sea floor) Question 2 The graphs for inflow and outflow you provided are plausible except for the fact that the level of the reservoir doesn't appear to be equal in Jan 1993 and Jan 1994. How can you tell? Basically, in order for the quantity of water to be equal in Jan 1993 and Jan 1994, we should have the TOTAL INFLOW of water during 1993 is equal to the TOTAL OUTFLOW. Now, the inflow and outflow graphs show the *rate* at which the water goes in and out of the reservoir. Therefore, TOTAL inflow and outflow are represented by the *areas* under each curve (in other words, we must take the integral of the inflow and outflow rates in order to get the inflow and outflow levels). We conclude that, in order for the quantity of water to be equal in Jan 1993 and Jan 1994, the area under each curve should be equal throughout 1993. In the graph you supplied, however, it appears that the outflow is larger than the inflow. You can seev this in the following colored graph, based on yours: http://img60.imageshack.us/img60/763/calcshit001boj9np1.jpg As you can see, the red area (total outflow) appears to be greater than the blue area (total inflow). Therefore, the quantity of water would be smaller in January 1994 than in January 1993. A correct version could something like this: http://img109.imageshack.us/img109/6004/inflowoutflowpw8.gif Notice that the area under both curves from Jan 1993 through Jan 1994 is roughly equal, implying that the quantity of water that went into the reservoir is approximately the same as the quantity that went out of it. Therefore, the quantity of water in the reservoir is roughly the same in Jan 1993 and in Jan 1994. Another feature of this graph is that the inflow is roughly cyclical, with a length of one year. This could make sense, given that the rainfall, which could be the only source of water for the reservoir, follows a cyclical pattern (more rain at certain times of the year and less rain at others). Finally, the outflow is lower in 1994. This can be rationalized by assuming the authorities are saving water for some purpose. It's clear from the graph that the quantity of water by mid-1994 is much higher than in Jan 1994. Question 3 You got these two 100% right. Great job! I hope this helps! If you have any doubt regarding my answer, please don't hesitate to request clarification before rating it. Otherwise, I await your rating and final comments. Best wishes! elmarto```
 jeremit-ga rated this answer: `Explained the answers well....made it all sound so easy!`  